The invention relates to techniques of identifying and classifying objects. More specifically, the present system describes using contextual information to improve statistical accuracy.
A common assumption made in the field of machine learning is that the examples are drawn independently from some joint input-output distribution.
Classical statistics begins with an assumption of a population distribution. Tiat population distribution describes how some attribute varies over a set of entities. The goal is to obtain information about the population distribution by sampling or by some other real world technique. It is often impractical to evaluate the parameters exactly. Therefore, one attempts, using the techniques of statistics, to obtain as much information as one can based on experimental evidence. Then all of the parameters can be viewed a coordinates of a single vector often called x . The value of x is fixed, but there is uncertainty about its value.
The population often has a distribution. For example, if the population has a Gaussian distribution, the parameters may have a mean value xcexc and a standard deviation xcexa3.
The Bayesian approach models the population by considering elements of the population to be randomly selected from a class of populations. Each class of the population is characterized by parameters that are under investigation. Bayesian analysis considers two parameters x and y. Bayesian analysis is largely an effort at determining the probability for the occurrence of the event y=xcex2 conditioned by the fact that x=xcex1 has occurred. During N trials the event x=xcex1 occurs nx(xcex1) times. The joint effect x=xcex1 and y=xcex2 occurs nxy (xcex1, xcex2) times.
The usual Bayesian approach assumes the distribution for x by looking at the trials for x. Hence, Bayesian analysis considers the trials in which x=xcex1. Once the random sampling processes are obtained, the notion of the random sampling process is extended by assuming that the class xi: 1 is less than or equal to I; is conditionally independent. Each of the xi have the same conditional distribution. This is because each of the xi are defined through the same random parameter x. While the events x and y are independent, both have the same conditional probabilities. Hence, the conditional probability that y=xcex2 given that x=xcex1 is independent of xcex1. This means that             P              x        |        y              ⁢          (              α        |        β            )        =                              P                      x            |            y                          ⁢                  (                      β            |            α                    )                    ⁢                        P          x                ⁢                  (          α          )                                    P        y            ⁢              (        β        )            
where the left part is the conditional probability that y=xcex2 given that x=xcex1, the right part is the conditional probability that x=xcex1 given that y=xcex2, px(xcex1) is the probability of xcex1 and px(xcex2) is the probability of xcex2.
Bayesian analysis is often used in estimator design. For instance, the conditional probability of a received message may be known and the conditional probability of the transmitted message is to be obtained. Bayesian analysis requires that the examples are drawn independently from the joint input/output distribution, as described above.
There are cases, however, where this no context assumption is not valid. One application where the independence assumption does not hold is the identification of white blood cell images. Abnormal cells are much more likely to appear in bunches than in isolation. Specifically, in a sample of several hundred cells, it is more likely to find either no abnormal cells or many abnormal cells than it is to find just a few. More generally, certain random processes are subject to xe2x80x9caliasingxe2x80x9d whereby they occur in clumps.
The present specification describes pattern classification in situations where an independence assumption is not necessarily correct. In such cases, the probability of identity of an object may be dependent on the identities of the accompanying objects. Those accompanying objects which provides the contextual information.
The techniques take into consideration the joint distribution of all the classes, and uses the joint distribution to adjust the object-by-object classification.
This method can be used in a number of settings. For example, the classification of white blood cells is improved by the use of contextual information.